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Drinks A and B are mixtures of lemon and orange juices. The ratio of l

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Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 26 Sep 2018, 00:09
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Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 26 Sep 2018, 02:36
7
Very interesting question. I would like to use: SMART NUMBER strategy, in which we use real numbers to avoid complex calculations.

Let's look at solution C, which is made from 4 parts of solution A and 1 part of solution B. Hence, you may want start with solution B.

Let's take 8ml of B, in which there are 5ml Lemon and 3ml Orange.
We need 8x4=32ml of A, in which there are 8ml Lemon and 24ml Orange.
Put A and B together, we have 13ml Lemon and 27ml Orange ==> D. 13/27
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Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 26 Sep 2018, 17:45
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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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Beqa chose an excellent method. +1

We can also find amounts of each juice in a 4:1 mix, and set them in a ratio

To find concentration of, say, OJ in A, sum the ratio parts.
Concentration = \(\frac{part}{total}=\frac{L}{L+OJ}\)

A mix: \(\frac{L}{OJ}=\frac{1}{3}\)
Total parts: (1 + 3) = 4
A, concentration of \(L = \frac{1}{4}\)
A, concentration of \(OJ=\frac{3}{4}\)

B mix: \(\frac{L}{OJ}=\frac{5}{3}\)
Total parts: (5 + 3) = 8
B, concentration of \(L = \frac{5}{8}\)
B, concentration of \(OJ=\frac{3}{8}\)

Drink A is mixed with drink B in the ratio of 4:1 to form drink C
So the amount of A in the resultant drink C is 4 times as much as B

Lemon juice only in 4A + 1B?

\((4)(\frac{1}{4})+(1)(\frac{5}{8})=\)

\((1+\frac{5}{8})=(\frac{8}{8}+\frac{5}{8})=\frac{13}{8}\)

Orange juice only in 4A+1B?
\((4)(\frac{3}{4})+(1)(\frac{3}{8})=\)

\((3+\frac{3}{8})=(\frac{24}{8}+\frac{3}{8})=\frac{27}{8}\)

Ratio of lemon juice to orange juice in C?
C = mix of 4A and 1B, as above

\(\frac{L}{OJ}=\frac{(\frac{13}{8})}{(\frac{27}{8})}=(\frac{13}{8}*\frac{8}{27})=\frac{13}{27}\)

Answer D
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Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 01 Oct 2018, 12:14
2
In A -
l -> 1/4 ------(A1)
O -> 3/4

In B -
l -> 5/8 ------ (A2)
o -> 3/8

let x be the Avg.

use weighted average formula -
w1/w2=(A2–Aavg)/(Aavg–A1)

(5/8 - x)/(x-1/4) = 4/1 --------- (this ratio is given in the question)
on solving =>
x=13/40
so lemon is 13
similarly solve for orange or we can just do 40-13=27
Answer should be 13:27 (D)
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Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 01 Oct 2018, 19:23
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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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let x=ratio of lemon juice to total drink C
4*1/4+1*5/8=5x
x=13/40
13/(40-13)=13/27=13:27 ratio of lemon juice to orange juice in drink C
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Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 03 Oct 2018, 16:39
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bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19


We have the following two ratios:

For A:

L : O = x : 3x

For B:

L : O = 5y : 3y

In drink C, we know the ratio of A : B is 4: 1; thus, we can set up the proportion:

(x + 3x)/(5y + 3y) = 4/1

4x/8y = 4

4x = 32y

x = 8y

If we let y = 1, then x = 8. So in drink A, we have L = 8 and O = 24, and in drink B, we have L = 5 and O = 3. So the total amount of L in drink C is 8 + 5 = 13 and the total amount of O in drink C is 24 + 3 = 27. So the ratio of L to O is 13/27.

Answer: D
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Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l  [#permalink]

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New post 05 Oct 2018, 05:57
bettatantalo wrote:
Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

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Little different approach:

\(Drink\) \(A\): \(\frac{1}{4}\) \(L\) \((lemon)\); \(Drink\) \(B\): \(\frac{5}{8}\) \(L\) \((lemon)\)

\(Drink\) \(C\): \(\frac{4}{5}Drink\) \(A\) and \(\frac{1}{5}Drink\) \(B\)

Therefore percentage of \(L\) in \(Drink\) \(C\) is:

\(\frac{4}{5}*\frac{1}{4} + \frac{1}{5}*\frac{5}{8} = \frac{13}{40}\)

Hence ratio of \(Lemon\) to \(Orange\) in \(Drink\) \(C\) is \(13:27\)
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Re: Drinks A and B are mixtures of lemon and orange juices. The ratio of l &nbs [#permalink] 05 Oct 2018, 05:57
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